12. According to the Huckel Molecular Orbital (MO) Theory for s bonding, the sccular determinant for MO energies for cycelopentadiene can be set up as
The polynomial f(x) can be factored into
f(x)=x⁵-5x³+5x+2=(x+2)(x²+ ax+6)²
What are "a" and "b" values?
(A) a =0； b=1
(B)a= 1； b=1
(C) a = -1； b=1
(D)a = 1； b=-1
(E) a = -1； b=-1

1. Define the operators, whereare the position and momentum operators. What is the value of the commutator? (hint: = =) (A)0 (B)1 (C) ih (D)h (E) 2h

2. What is the , for a non-ideal gas whose state can be expressed as the virial equation: (V=molar volume)? (A) (B)(C)(D)(E)

3. Which valence bond wavefunction for He is not a proper wavefunction because it violates the Pauli exclusion principle? (Please note: the numbers 1 and 2 represent the two electrons of He, N is the normalization constant, 1sA and 1Se represent the atomic orbitals, and a and B are spin wavefunctions.) (A) φ(1,2) = N[1sA(1)1sB；(2)-1SA(2)1sB(1)][a(1)B(2)-a(2)B(1)] (B)φ(1,2)=N[1sA(1)1sB(2)+1sA(2)1sB(1)][a(1)B(2)-a(2)B(1)] (C) φ(1,2)=N[1sA(1)1sB(2)-1sA(2)1SB(1)][(1)β(2)+a(2)β(1)] (D)φ(1,2)=N[1sA(1)1sB(2)-1sA(2)1SB(1)][a(1)a(2)] (E)φ(1,2)=N[1sA(1)1sB(2)-1SA(2)1SB(1)][β(1)β(2)]

4. We can construct three sp2 hybrid orbitals (i.e., φun = 1,2,3) as follows:φ1=a1(2s)+b1(2pz)φ2=a2(2s)+b2(2pz)+c2(2px)φ3 =a3(2s)+b3(2pz)+c3(2px)where 2s,2px and 2pz are normalized atomic orbitals and an,bn and cn are constants. Assume these hybrid orbitals are normalized and orthogonal to each other, then which of the following is incorrect. (A)a1 = a2 = a3 = (B)b1= (C)b2 =b3 =- (D)c2=c3 = (E)=1

5. According to the selection rules in the atomic spectra, which of the following transition is NOT allowed. (A) 2P3/2→2S1/2 (B) 2D3/2→2P1/2 ,→ 2P1/2 (C) 2D5/2→2P1/2 (D) 2P1/2→2S1/2 (E) 2D5/2→2P3/2

6. Two metal blocks with the same mass at different temperatures (T1 and T2) are contacting each other the reach the same temperature. What is AS assuming no heat loss during heat transfer.(A) (B) (C)(D)(E)

7. The first few spherical harmonics(θ, Φ) responsible for the angular parts of the hydrogen wavefunctions are listed below.Which combination of spherical harmonics (θ,Φ) can give you the py orbital?hint: Euler formula e±inΦ = cos(nΦ) isin(nΦ) (A) (B) (C) (D)(E)

8. An unnormalized wavefunction of the hydrogen atom is given by r2e(3 cos2 θ - 1). What are the three quantum numbers (n, I, m) associated with this orbital? (A) (2,2,0) (B)(2,1,1) (C) (3,2,0) (D) (3,1,1) (E) none of the above. 

9. The general structure of the porphyrin molecule is shown on the right side. This molecule is planar and so we can approximate the π electrons as being confined in a square with the length a = 10 The porphyrin molecule has "22"π electrons. According to the particle in a two-dimensional (2D) box, the energy states are given bywhere nx and ny are quantum numbers. Assume that each energy levet in the box is capable of holding no more than two electrons. What is the electronic transition responsible for the promotion of an electron from the highest filled energy level to the lowest empty energy level? (A) E(3,3)→E(4,2) (B)E(3,2)→E(4,1) (C) E(2,3) → E(2,4) (D) E(3,3)→E(4,3) (E) E(3,4) → E(4,4)

10. Following the question 09, what is the transition energy for an electron from the highest filled level to the lowest empty level? (A)8091 cm-1 (B) 11006 cm-1 (C) 7240 cm-1  (D)9230 cm-1  (E) 6061 cm-1 

113年 - 113 台灣聯合大學系統_碩士班招生考試_化學類:物理化學#122381

110年 - 110 國立臺灣科技大學_碩士班招生試題_材料科學與工程系(甲組)：物理化學#105493

110年 - 110 國立清華大學碩士班考試入學試題_生醫工程與環境科學系/丙組(應用化學組):物理化學#104980

110年 - 110 國立清華大學碩士班考試入學試題_生命科學院/丙組(計算生物與人工智慧組):物理化學#104956

110年 - 110台灣聯合大學系統_碩士班招生考試_化學類:物理化學#104949

110年 - 110 高雄科技大學_碩士班招生考試_化學工程與材料工程系：物理化學(乙組)#104402

110年 - 110 國立臺北科技大學_碩士班招生考試_化學工程與生物科技系化學工程碩士班(乙組)：物理化學#103868

110年 - 110 國立臺灣大學_碩士班招生考試_部分系所:物理化學(A)(基礎熱力學與反應動力學)#102143

110年 - 110 國立宜蘭大學_碩士班招生考試_化學工程與材料工程學系：物理化學(含熱力學與動力學)#102135

110年 - 110 國立臺灣大學_碩士班招生考試_藥學、口腔生物科學研究所:物理化學(B)#101963